Sky High 1972

In this dexterity game, players build a tower out of variously shaped wooden blocks based upon dice rolls. The results of a roll table indicate whether you must try to use all the blocks left in the kitty, or only one block. Often, the result of the roll indicates the shape of a block that you must place on top of the tower. Completing the tower grants you 15 points, causing the tower to collapse on your turn grants all the other players points equal to the number of blocks left in the kitty. There is an exception: if you fail in your attempt to place the very last block atop the tower, each other player gets 15 points. The game is played to a 50 point total.

The year, 1972, is a guess, as the game is unmarked. However the box is very similar to "Penta-Logics," which did come out in 1972, hence the guess.